Question

The graph shown here is the graph of which of the following rational functions ?

Answer 1

The correct options is (A)
`f(x) = (x-2)/((x+1)(x-3))`

Explanation:

Consider the provided graph:

The provided graph has vertical asymptotes at x = -1 and x = 3.

Therefore, denominator must contain x + 1 and x - 3.

Also, at x = 2 the graph intersect the x axis that means at x = 2, y = 0

Therefore, the rational function must contain x - 2 in numerator.

Hence, the correct options is (A) because it contain x + 1 and x - 3 in denominator and x - 2 in numerator.

Answer 2

The first thing you should do for this case is to study the domain of the function to verify the values of x for which it is defined.
We have then the domain of the function is:
x = (- inf, -1)
x = (- 1, 3)
x = (3, inf)
Equivalently all the x that belong to:
(-inf, -1) U (-1, 3) U (3, inf)
Therefore, the function is:
F (x) = (x-2) / ((x + 1) * (x-3))
answer
A. F (x) = (x-2) / ((x + 1) * (x-3))